Canted Antiferromagnetic Order of Imbalanced Fermi-Fermi mixtures in Optical Lattices by Dynamical Mean-Field Theory

We investigate antiferromagnetic order of repulsively interacting fermionic atoms in an optical lattice by means of Dynamical Mean-Field Theory (DMFT). Special attention is paid to the case of an imbalanced mixture. We take into account the presence of an underlying harmonic trap, both in a local density approximation and by performing full Real-Space DMFT calculations. We consider the case that the particle density in the trap center is at half filling, leading to an antiferromagnetic region in the center, surrounded by a Fermi liquid region at the edge. In the case of an imbalanced mixture, the antiferromagnetism is directed perpendicular to the ferromagnetic polarization and canted. We pay special attention to the boundary structure between the antiferromagnetic and the Fermi liquid phase. For the moderately strong interactions considered here, no Stoner instability toward a ferromagnetic phase is found. Phase separation is only observed for strong imbalance and sufficiently large repulsion.Comment: 7 pages, 5 figures, published versio

Self-Consistent Theory of Anderson Localization: General Formalism and Applications

The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered solids, the regimes of weak and strong localization are discussed. Then the scaling theory of the Anderson localization transition is reviewed. The renormalization group theory is introduced and results and consequences are presented. It is shown how scale-dependent terms in the renormalized perturbation theory of the inverse diffusion coefficient lead in a natural way to a self-consistent equation for the diffusion coefficient. The latter accounts quantitatively for the static and dynamic transport properties except for a region near the critical point. Several recent applications and extensions of the self-consistent theory, in particular for classical waves, are discussed.Comment: 25 pages, 2 figures; published version including correction

Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy

The importance of Hund's rule coupling for the stabilization of itinerant ferromagnetism is investigated within a two-band Hubbard model. The magnetic phase diagram is calculated by finite-temperature quantum Monte Carlo simulations within the dynamical mean-field theory. Ferromagnetism is found in a broad range of electron fillings whereas antiferromagnetism exists only near half filling. The possibility of orbital ordering at quarter filling is also analyzed.Comment: 5 pages, 6 figures, RevTeX, final version contains an additional phase diagram for smaller Hund's rule coupling. to appear in Eur. Phys. J. B (1998

Superfluid Helium 3: Link between Condensed Matter Physics and Particle Physics

The discovery of the superfluid phases of Helium 3 in 1971 opened the door to one of the most fascinating systems known in condensed matter physics. Superfluidity of Helium 3, originating from pair condensation of Helium 3 atoms, turned out to be the ideal testground for many fundamental concepts of modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and their spontaneous breakdown, topological defects, etc. Thereby the superfluid phases of Helium 3 enriched condensed matter physics enormously. In particular, they contributed significantly - and continue to do so - to our understanding of various other physical systems, from heavy fermion and high-Tc superconductors all the way to neutron stars, particle physics, gravity and the early universe. A simple introduction into the basic concepts and questions is presented.Comment: 11 pages, 2 figures; to be published in Acta Physica Polonica B [Proceedings of the XL Jubilee Cracow School of Theoretical Physics on "Quantum Phase Transitions in High Energy and Condensed Matter Physics"; 3-11 June, 2000, Zakopane, Poland

Ferromagnetism and non-local correlations in the Hubbard model

We study the possibility and stability of band-ferromagnetism in the single-band Hubbard model for the simple cubic (SC) lattice. A non-local self-energy is derived within a modified perturbation theory. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of k-dependence. The importance of non-local correlations for the fulfillment of the Mermin-Wagner theorem is our main result. A phase digram showing regions of ferromagnetic order is calculated for the three dimensional lattice. Besides, we show results for the optical conductivity and prove that already the renormalized one-loop contribution to the conductivity cancels the Drude peak exactly in case of a local self-energy which is not anymore true for a non-local self-energy.Comment: 11 pages, 10 figures, accepted for publication in PR

Anderson impurity in a correlated conduction band

We investigate the physics of a magnetic impurity with spin 1/2 in a correlated metallic host. Describing the band by a Hubbard Hamiltonian, the problem is analyzed using dynamical mean-field-theory in combination with Wilson's nonperturbative numerical renormalization group. We present results for the single-particle density of states and the dynamical spin susceptibility at zero temperature. New spectral features (side peaks) are found which should be observable experimentally. In addition, we find a general enhancement of the Kondo scale due to correlations. Nevertheless, in the metallic phase, the Kondo scale always vanishes exponentially in the limit of small hybridization.Comment: Final version, 4 pages RevTeX, 8 eps figures include

T-matrix formulation of real-space dynamical mean-field theory and the Friedel sum rule for correlated lattice fermions

We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.Comment: 7 pages, no figures, extended and corrected versio

Isosbestic Points: Theory and Applications

We analyze the sharpness of crossing ("isosbestic") points of a family of curves which are observed in many quantities described by a function f(x,p), where x is a variable (e.g., the frequency) and p a parameter (e.g., the temperature). We show that if a narrow crossing region is observed near x* for a range of parameters p, then f(x,p) can be approximated by a perturbative expression in p for a wide range of x. This allows us, e.g., to extract the temperature dependence of several experimentally obtained quantities, such as the Raman response of HgBa2CuO4+delta, photoemission spectra of thin VO2 films, and the reflectivity of CaCu3Ti4O12, all of which exhibit narrow crossing regions near certain frequencies. We also explain the sharpness of isosbestic points in the optical conductivity of the Falicov-Kimball model and the spectral function of the Hubbard model.Comment: 12 pages, 11 figure